Problem: Harry's spell casting class lasts for $2\dfrac{5}{6}$ hours each day. Today, he has been in the class for $1\dfrac{2}{5}$ of an hour so far. How much more time is left in the class?
To find the time left in class, we can subtract. $2\frac56$ $1\frac{2}{5}$ $?$ Length of casting class Time in class Time left in class $2\dfrac{5}{6}} - {1\dfrac{2}{5}}$ Our denominators need to be the same so we can subtract What is the least common multiple for the denominators $6}$ and ${4}$ ? The least common multiple of $D6$ and ${5}$ is ${30}$. $\dfrac{5}\times5}{6}\times5} = \dfrac{25}{30}}$ $\dfrac{{2}\times6}{{5}\times6} = {\dfrac{12}{30}}$ Now, let's subtract our fractions. $\begin{aligned} &2} &\dfrac{25}{30}}\\\\ -&{1}&{\dfrac{12}{30}}\\ \hline\\ &&{\dfrac{13}{30}} \end{aligned}$ Last, let's subtract our whole numbers. $\begin{aligned} &2} &\dfrac{25}{30}}\\\\ -&{1}&{\dfrac{12}{30}}\\ \hline\\ &1&{\dfrac{13}{30}} \end{aligned}$ There is $1\dfrac{13}{30}$ hours left in class. This can also be written as $\dfrac{43}{30}$.